-2000x^2+16000x-5000=0

Solution for -2000x^2+16000x-5000=0 equation:

-2000x^2+16000x-5000=0

a = -2000; b = 16000; c = -5000;
Δ = b2-4ac
Δ = 160002-4·(-2000)·(-5000)
Δ = 216000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216000000}=\sqrt{36000000*6}=\sqrt{36000000}*\sqrt{6}=6000\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16000)-6000\sqrt{6}}{2*-2000}=\frac{-16000-6000\sqrt{6}}{-4000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16000)+6000\sqrt{6}}{2*-2000}=\frac{-16000+6000\sqrt{6}}{-4000}
$